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yet another maths problem
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| dukes |
ok anyone happen to know how to find the genral solution to a ordinary differential equations (ODE's)
like how would i go about finding the genral solution of the ODE
ds/dt = s + 1
what is the methods i would follow to solve problems of a similar nature? |
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| Omegasox |
| We need a Homework forum. And a forum where you can post essays for others to use. :D |
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| Neo nEro |
You need an intigrating factor
ds/dt - s = 1
IF = -1
which is exp(int(-1,t))=exp(-t)
then multiply that to the whole equation
so
ds/dt*exp(-t) - s*exp(-t) = exp(-t)
now the left hand side is a derivative:
d(s*exp(-t))/dt= exp(-t)
so you intigrate both sides and then divide by the exp(-t)
which gives you:
s*exp(-t) = -exp(-t)+C
so s= -1+C/exp(-t)= -1+C*exp(t) |
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| dukes |
| quote: | Originally posted by Neo nEro
You need an intigrating factor
ds/dt - s = 1
IF = -1
which is exp(int(-1,t))=exp(-t)
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how do you find a sutable integrating factor?
its not really the answer to the question im after as much as how to answer these questions. |
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| caddyshack |
| quote: | Originally posted by dukes
how do you find a sutable integrating factor?
its not really the answer to the question im after as much as how to answer these questions. |
if its a first order liner equation then the integrating factor is the junk in front of the s term once the equation is in standard form |
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| dukes |
i think im gonna give up because im never gonna learn this in time to hand in my coursework.
i may beable to grasp how to do that question (i still am a little confused with it but the next one is a tad more complicated. as in i cant get it in the form
ds/dt + s = ??
and such.
arg should have been to uni more :( |
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| caddyshack |
| quote: | Originally posted by dukes
i think im gonna give up because im never gonna learn this in time to hand in my coursework.
i may beable to grasp how to do that question (i still am a little confused with it but the next one is a tad more complicated. as in i cant get it in the form
ds/dt + s = ??
and such.
arg should have been to uni more :( |
you want it in the form 1*s' + f(t)*s = g(t)
e^int(f(t)) is your integrating factor
all this is in your book some place |
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| Resnick |
| laplace transform it...its by far the easiest way...and if u dont know what that is just look up the rules for it in some book...it will make ur life a billion times easier |
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| Noctone |
| Separation of variables is the simplest way to solve this problem. Laplace transform would also be very easy, but just slightly more complex. |
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| Massive84 |
| quote: | Originally posted by Neo nEro
You need an intigrating factor
ds/dt - s = 1
IF = -1
which is exp(int(-1,t))=exp(-t)
then multiply that to the whole equation
so
ds/dt*exp(-t) - s*exp(-t) = exp(-t)
now the left hand side is a derivative:
d(s*exp(-t))/dt= exp(-t)
so you intigrate both sides and then divide by the exp(-t)
which gives you:
s*exp(-t) = -exp(-t)+C
so s= -1+C/exp(-t)= -1+C*exp(t) |
how do you use this in real life :S, always found that a more intresting question than the equation it self @ school. |
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| caddyshack |
| quote: | Originally posted by Noctone
Separation of variables is the simplest way to solve this problem. Laplace transform would also be very easy, but just slightly more complex. |
can't seperate variables |
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| caddyshack |
| quote: | Originally posted by Massive84
how do you use this in real life :S, always found that a more intresting question than the equation it self @ school. |
well this equation could describe the motion of a car in response to pushing the gas or maybe the current through a circuit. making it possible for you to have the freedom of a car and listen to music respectively |
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